Parents in London are learning if their children have got a place in the primary school of their choice - around 6,000 of the 100,000 who applied will have failed to get into a single one of their preferred schools.
Steph Neale, head teacher at Beatrix Potter Primary School South London, told the Today programme's John Humphrys that they have 369 applicants for 60 places at their school this year.
"There's a lot of children being born in London. Where they go is a good question," he said.
He went on to say that a lot of the time, "the council takes the flack" and attempt to expand already popular schools, but pointed out that "you can't expand schools ad infinitum because it becomes unmanageable".
David Simmonds, education spokesman at the Local Government Association, said between 2010 and 2015 it is estimated that England needs 450,000 more school places and as many as 800,000 by 2020.
He said that most extra capacity this will come down to councils trying to expand existing popular schools or building new schools from scratch.
Despite the problems, he insisted that local authorities "have been quite well prepared", adding that the "vast majority" of children get into one of their parents' six preferred primary schools.
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